Abstract：In this paper，it is pointed out that the topology optimization of continuum structures had entered a new stage since Zhou’s research in 2016. The new stage includes two points: (1) Designs of discrete structures have been benefitted from the results of the topology optimization of continuum structures. (2)At the same time, the theory of topology optimization of continuum structures can benefit from the topology optimization of discrete structures. The rational criterion of the pre-estimation distribution of failure regions is established based on geometrical analysis, that is, the upper limit and lower limit of the size of the local failure mode and the upper limit and lower limit of the space of adjacent local failure regions are given. The advantages and disadvantages of the pre-estimation distribution strategies of failure regions proposed by Janson and Zhou are analyzed according to the proposed rational criterion. Numerical examples are given to verify the relevant strategies. The results show that Janson’s strategy is too conservative to lead to unnecessary computation. Zhou's strategy with the gapless fill of failure regions can’t guarantee that all discrete members yielded by topology optimization pass the failure test, but in most cases, the optimal topology with sufficient redundancy can be obtained. While the pre-estimation distribution of failure regions satisfies the proposed rational criterion, all discrete members yielded by topology optimization can be ensured to pass the failure test and optimal topology with more redundant can be achieved. The study shows that the rational criterion for the pre-estimation distribution of failure regions provides theoretical progress in describing local failure regions for the failure-safety topology optimization continuum structures.
2018, Vol. 39 
